Three scale thermomechanical theory for swelling biopolymeric systems

A three-scale theory for the swelling polymeric/biopolymeric media is developed via the hybrid mixture theory. At the microscale, the solid polymeric matrix interacts with the solvent through surface contact. At the mesoscale, the homogeneous mixture of vicinal fluid and solid polymers exchanges thermodynamic properties with two bulk fluids, one of which is of the same type as the vicinal fluid. The relaxation processes within the polymeric matrix are incorporated by modeling the solid phase as viscoelastic and the solvent phases as viscous at the macroscale. We obtain novel equations for the total stress tensor, chemical potential of the solid phase, heat flux and Darcy's law all at the macroscale. Viscoelastic stress components in Darcy's law make it applicable for both Fickian and non-Fickian fluid transport. The form of the generalized Fick's law is similar to that obtained in earlier works involving colloids. Thermoviscoelastic and thermoviscous effects are incorporated by coupling thermal gradients with strain-rate tensors for the solid phase and the deformation-rate tensors for the liquid phases.     

Non-Darcian Airflow through Ceramic Foams

This paper presents the first results on fluid flow through (laboratory-made) ceramic foams. Pressure drop (ΔP) vs airflow rate ( U ) measurements show that Darcy's law does not hold and that the non-Darcian airflow through the foams satisfies an equation of the form ΔP = aU + bU ². A permeability quotient is defined, which appears to be a qualitative measure for the average pore size of a foam. A Reynolds number defined in terms of this quotient can be used to estimate the Darcian flow range for a certain fluid.     

Gas permeation and viscoelastic deformation of prepregs in composite manufacturing processes

Gas permeation and creep deformation of a commercial prepreg, which exhibits viscoelastic characteristics, were investigated as a function of time, temperature, and consolidation pressure. Experiments using a prepreg stack demonstrated that the material exhibited a linear viscoelastic bulk deformation under vacuum/autoclave pressure and furthermore, the in-plane gas flow exhibited non-Darcian flow behavior with a permeation hysteresis. This behavior was viewed and analyzed by two viscoelastic relaxation processes: (1) bulk dimensional relaxation, and (2) microscopic pore structure rearrangement. A modified standard linear solid (SLS) viscoelastic model was used to interpret the creep compliance and dynamic gas permeability utilizing two independent relaxation parameters. By visual investigation of pore sizes and their distribution, air permeation was found to take place mostly through the interlaminar porosity network for the prepreg system examined.     

Transient forced convection in the entrance region of a porous tube

The problem of transient forced convection in the entrance region of a cylindrical porous medium with developing thermal boundary layer is investigated. The hydrodynamic behaviour of the flow is assumed to be steady and fully developed, and both Darcian and non-Darcian effects on the flow are considered. Thermal transients are created by a step change in the temperature of the tube wall. The effect of different fluid and solid-matrix parameters on Nusselt number, thermal entrance length, total heat absorbed and mixing cup temperature are considered.     

Dr. James A. Koutsky 1940-1994

James A. Koutsky, Professor in the Chemical Engineering Department at the Univer- sity of Wisconsin, died on November 25,1994. He was born on December 1,1940, in Parma, Ohio, the son of Joseph and Marion Koutsky. Dr. Koutsky received B. S., M. S. degrees (both in Chemical Engineering) and a Ph.D. in Polymer Science, all from Case Western Reserve University.     

Transient forced convection in the entrance region of porous concentric annuli

The problem of transient laminar forced convection in the entrance region of a porous concentric annulus with developing thermal boundary layer is solved numerically by the finite difference technique. The hydrodynamic behaviour of the flow is assumed to be steady and fully developed, and both Darcian and non-Darcian effects on the flow are considered.     

混炼机横截面PP熔体液滴分散过程的数值模拟研究

对Fluent进行二次开发,通过用户自定义函数,将黏弹性流体的动量方程和变形张量输运方程加载到Fluent中,从而实现了对聚合物黏弹性流体流动的模拟。采用VOF界面追踪方法,对聚合物熔体中的单个液滴在混炼机横截面流场作用下发生的变形、破碎行为和二次团聚过程进行了分析研究。探讨了液滴在混炼腔复杂流场中的分散过程和微观结构的形成机理,对揭示共混改性过程中分散相织态结构发展演变过程和机理具有指导意义。结果表明,PP液滴在混炼过程中经历了变形、破碎、聚并过程;PP液滴在C形区发生了不均匀变形行为,在相互作用窗混沌流场下发生了拉伸、挤压、交叉行为;PP液滴的破碎行为包括毛细不稳破碎、末端夹断以及在螺棱背风面的松弛破碎。     

CFD simulation of bubble columns incorporating population balance modeling

A computational fluid dynamics (CFD)-code has been developed using finite volume method in Eulerian framework for the simulation of axisymmetric steady state flows in bubble columns. The population balance equation for bubble number density has been included in the CFD code. The fixed pivot method of Kumar and Ramkrishna [1996. On the solution of population balance equations by discretization—I. A fixed pivot technique. Chemical Engineering Science 51, 1311-1332] has been used to discretize the population balance equation. The turbulence in the liquid phase has been modeled by a k-ε model. The novel feature of the framework is that it includes the size-specific bubble velocities obtained by assuming mechanical equilibrium for each bubble and hence it is a generalized multi-fluid model. With appropriate closures for the drag and lift forces, it allows for different velocities for bubbles of different sizes and hence the proper spatial distributions of bubbles are predicted. Accordingly the proper distributions of gas hold-up, liquid circulation velocities and turbulence intensities in the column are predicted. A survey of the literature shows that the algebraic manipulations of either bubble coalescence or break-up rate were mainly guided by the need to obtain the equilibrium bubble size distributions in the column. The model of Prince and Blanch [1990. Bubble coalescence and break-up in air-sparged bubble columns. A.I.Ch.E. Journal 36, 1485-1499] is known to overpredict the bubble collision frequencies in bubble columns. It has been modified to incorporate the effect of gas phase dispersion number. The predictions of the model are in good agreement with the experimental data of Bhole et al. [2006. Laser Doppler anemometer measurements in bubble column: effect of sparger. Industrial & Engineering Chemistry Research 45, 9201-9207] obtained using Laser Doppler anemometry. Comparison of simulation results with the experimental measurements of Sanyal et al. [1999. Numerical simulation of gas-liquid dynamics in cylindrical bubble column reactors. Chemical Engineering Science 54, 5071-5083] and Olmos et al. [2001. Numerical simulation of multiphase flow in bubble column reactors: influence of bubble coalescence and breakup. Chemical Engineering Science 56, 6359-6365] also show a good agreement for liquid velocity and gas hold-up profiles.     

Translational Oscillatory Motions of a Porous Spherical Shell with a Solid Impermeable Core in a Viscous Fluid

Theoretical Foundations of Chemical Engineering - Analytical solutions of the non-steady-state Brinkman equation that describes the flow of a fluid inside a porous spherical shell with a solid...     

A drag force closure for uniformly dispersed fluidized suspensions

The present study is concerned with the problem of closure for the drag force with regard to fluidized suspensions of uniformly dispersed spherical particles. A new closure relationship, based on the empirical correlation by Richardson and Zaki [1954. Sedimentation and fluidization: Part I. Transactions of the Institution of Chemical Engineers 32, 35] is derived. The main distinctive feature of the equation advanced by the authors is its being consistent with the Richardson and Zaki correlation over the whole range of fluid dynamic regimes and for any value of the fluid volume fraction. This property, usually not met by the equations of closure currently used in multiphase fluid dynamics, is nonetheless essential when simulating the motion of fluidized suspensions as it ensures a more accurate prediction of the expansion profiles of homogeneous systems, a feature that indirectly reflects a better assessment of the drag force magnitude. The article contains a brief critical overview on some closure relationships commonly employed in most computational fluid dynamics commercial codes, more specifically those based on the work by Ergun [1952. Fluid flow through packed columns. Chemical Engineering Progress 48, 89], Di Felice [1994. The voidage function for fluid-particle interaction systems. Internation Journal of Multiphase Flow 20, 153], Kmiec [1982. Equilibrium of forces in a fluidized bed—experimental verification. Journal of Chemical Engineering 23, 133], Lewis et al. [1949. Characteristics of fluidized particles. Industrial and Engineering Chemistry 41, 1104] and Wen and Yu [1966. Mechanics of fluidization. Chemical Engineering Progress Symposium Series 62, 100]. Furthermore, to test the validity of the equation herein proposed, its predictions are compared with experimental data obtained for homogeneous assemblies of spherical particles reported in literature and based on the work by Happel and Epstein [1954. Viscous flow in multiparticle systems: cubical assemblages of uniform spheres. Industrial and Engineering Chemistry 46, 1187], Richardson and Zaki [1954. Sedimentation and fluidization: Part I. Transactions of the Institution of Chemical Engineers 32, 35], Rumpf and Gupte [1971. Einflüsse der porosität und korngrößenverteilung im widerstandsgesetz der porenströmung. Chemie Ingenieur Technik 43, 367] and Wilhelm and Kwauk [1948. Fluidization of solid particles. Chemical Engineering Progress 44, 201]. A good agreement is found between theoretical results and experimental values.     

表面活性剂虫状胶束流体中颗粒沉降负尾迹模拟

颗粒在剪切稀释黏弹性表面活性剂形成的蠕虫状胶束流体中沉降时会产生负尾迹,负尾迹的形成对该种复杂流体与固体颗粒之间的相互作用具有重要影响。基于Giesekus本构方程,采用POLYFLOW软件模拟了黏弹性表面活性剂(Viscoelastic Surfactant, VES)蠕虫状胶束流体中单颗粒的沉降过程,分析了流体松弛时间和迁移因子对颗粒周围速度场及应力场的影响,重点研究了颗粒尾部速度负尾迹的产生原因及其对颗粒曳力的影响。结果表明,Giesekus本构方程能够描述VES流体的非线性剪切变稀行为和弹性导致的拉伸变形。流体弹性导致颗粒尾部产生较大的拉伸变形,剪切稀化和流体弹性的共同作用使颗粒尾部产生拉伸变形,导致负尾迹出现。表征流体弹性的De(黛博拉数)越大,流体拉伸黏度的Tr(特劳顿数)越小,负尾迹越长。负尾迹的出现使VES流体中颗粒所受曳力减小,沉降速度开始增加。模拟结果为此种流体的进一步应用提供了一定的研究基础。     

Velocity profiles and circulation in Stefan-diffusion

Recently, a new multicomponent fluid transport theory was presented by Kerkhof and Geboers [2005a. Towards a unified theory of isotropic molecular transport phenomena. A.I.Ch.E. Journal 51, 79-121], in which the transport is described by simultaneous equations of motion for each species. The theory is applied to water vapor and nitrogen in the Stefan tube as an example of two-dimensional fluid transport. Numerical solution results in axial and radial velocity profiles for both species and clearly indicates circulation of nitrogen. Comparison with the classic Stefan-diffusion equation shows that for wide tubes the latter approach is still reasonable, but for narrow tubes shear effects dominate. The nitrogen circulation causes radial concentration profiles. For small diameter tubes, the axial velocity profiles from the present model are close to those from the velocity profile model of Kerkhof et al. [2001. On the isothermal binary transport in a single pore. Chemical Engineering Journal 83, 107-121], in which radial transport was assumed to be infinitely fast.     

Assessment of Forchheimer's Equation to Predict the Permeability of Ceramic Foams

Correct estimation of the pressure drop in filtration processes that involve fluid velocity variations is of major importance, because it allows the filtration rate and/or the energy consumed on fluid flow to be more accurately controlled. Permeability of porous filters has been often described by Forchheimer's equation, which establishes a nonlinear dependence between pressure drop and fluid velocity. Two constants, k ₁ and k ₂, dependent only on the medium, quantify the viscous and inertial effects on the pressure drop curve. In this work, experimental data of airflow through 10 pores per linear inch ceramic foam filters are used to show that a single sample may have completely distinct permeability constants depending on the data range chosen for analysis. The Darcian permeability constant k ₁ displays higher variation than the non-Darcian permeability constant k ₂. The conclusion is that special attention must be taken to represent permeability of highly porous structures in a large velocity range. The predictability of Forchheimer's equation generally worsens when less data are included in the curve fitting, particularly at low velocities. Careful consideration should be made if constants k ₁ and k ₂ are intended to be used for permeability estimation beyond the fitting range.     

理想流体柏努利方程在化工原理教学中的应用

在化工原理教学中,理想流体伯努利方程能够帮助学生理解流体的能量转换与守恒特性。本文提出了由理想流体到一般流体逐步导出伯努利方程的方法,给出了两种适合于不同层次教学需要的伯努利方程的推导过程,一种强调了数学的严格性和规范性,另一种旨在加深学生对能量守恒和流体运动过程的理解。     

Combined effects of internal heat generation and higher order chemical reaction on the non‐darcian forced convective flow of a viscous incompressible fluid with variable viscosity and thermal conductivity over a stretching surface embedded in a porous medium

In this paper, we study the combined effects of internal heat generation and higher order chemical reaction on a steady two‐dimensional non‐Darcian forced convective flow of a viscous incompressible fluid with variable dynamic viscosity and thermal conductivity in a fluid saturated porous medium passing over a linear stretching sheet. Using similarity transformations, the governing nonlinear‐coupled partial differential equations are made dimensionless and solved numerically for similarity solutions using very robust computer algebra software Maple 8. The non‐dimensional velocity, temperature and concentration distributions are presented graphically for various pertinent parameters such as relative temperature difference parameter, Darcy number, porosity parameter, reaction rate parameter and the order of the chemical reaction. The variations of Prandtl number and Schmidt number within the boundary layer are also displayed graphically when the fluid dynamic viscosity and thermal conductivity are temperature dependent. From the present numerical computations it is found that Prandtl number as well as Schmidt number must be taken as variables within the flow domain when the fluid's dynamic viscosity and thermal conductivity are variable. In the presence of internal heat generation, dynamic viscosity and thermal conductivity of the fluid are found to be higher than when it is absent. Increasing Darcy number reduces dynamic viscosity as well as thermal conductivity whereas increasing pore size reduces the Schmidt number and increases the Prandtl number within the boundary layer. For higher order reaction the rate of increase in mass transfer function is less compared to the rate of increase for the lower order reaction. © 2011 Canadian Society for Chemical Engineering     

非牛顿流体搅拌流场的数值模拟研究进展

对非牛顿流体搅拌流场数值模拟过程中的控制方程、旋转桨叶的处理以及数值计算方法三个方面进行了综合论述。阐述了广义牛顿流体模型形式简单、计算量低,在非牛顿流体搅拌流场数值模拟过程中应用广泛;黏弹性流体本构方程具有高度的非线性,采用计算流体力学(CFD)方法对其搅拌流场进行数值模拟难度较高,目前仍处于起步阶段;通过合理简化黏弹性流体本构方程以及采用恰当的数值离散方法,有助于在黏弹性流体的搅拌流场数值模拟中取得进展。     

Onset of pulsing in trickle beds with non-Newtonian liquids at elevated temperature and pressure—Modeling and experimental verification

The onset of pulse flow in trickle-bed reactors involving gas-non-Newtonian liquid systems was predicted from a stability analysis of the solutions around equilibrium steady-state trickle flow of a transient two-fluid model based on the volume-average mass and momentum balance equations. The model was developed for the versatile Herschel-Bulkley constitutive rheological equation from which special solutions for plastic Bingham fluids, power-law shear-thinning and thickening fluids, as well as Newtonian fluids were derived. The impact of yield stress, consistency and power-law indices, and temperature and reactor pressure on the trickle-to-pulse flow transition was analyzed theoretically. Model predictions of the trickle-to-pulse transition for gas-non-Newtonian liquid systems were confronted with elevated temperature and pressure experimental transition data obtained for air-0.25 and 0.5 mass(carboxymethylcellulose) CMC solution systems measured by means of an electrical conductivity technique. In addition the model version offspring corresponding to the Newton case (n=1,k=μ_?,τ₀=0), confronted with measured high temperature/pressure-transition data from this work and high-pressure transition data from Wammes et al. [1990. The transition between trickle flow and pulse flow in a cocurrent gas-liquid trickle-bed reactor at elevated pressure. Chemical Engineering Science 45, 3149; 1991. Hydrodynamics in a cocurrent gas-liquid trickle bed at elevated pressures. A.I.Ch.E. J. 37, 1849] and Burghardt et al. [2002. Hydrodynamics of a tree-phase fixed-bed reactor operating in the pulsing flow regime at an elevated pressure. Chemical Engineering Science 57, 4855] proved equally successful.     

On the mechanisms for drag reduction: A viscoelastic evaluation based on a bead-spring model

Two possible drag reduction mechanisms were examined by studying the viscoelastic effects of polymer solutions for the separate cases of oscillatory shear flow and elongational flow. The constitutive equation used was based on a modified dumbbell molecular model which predicts non-Newtonian viscosity and both the primary and the secondary normal stress differences. It can be shown that when this constitutive equation is arranged in the form of the Oldroyd model, the latter becomes a special case of this more general equation. The present results show that viscoelastic effects on the mean local rate of energy dissipation of a fluid element in an oscillatory motion are negligibly small. However, such effects introduce very large increases in the elongational viscosity as the stretching rate exceeds a certain limiting value and the flow time exceeds the terminal relaxation time of the fluid. The relative merits of these findings as possible explanations of turbulent drag reduction are briefly discussed.     

化工单元操作设计计算解析

化工单元操作设计计算是化工原理课程的核心内容,本文以流体流动、传热、吸收和精馏单元操作为例,分析了不同单元操作设备设计计算的共性.尽管各单元操作内容不同,设计计算方法各异,但采用的公式有三类:衡算方程,过程速率方程和相平衡方程.理解了这一点,对化工原理的学习很有帮助.